Tag Archives: Scaffolding

Thanks to a recent tweet by Dylan Wiliam, and a great article that it linked to by Michael Pershan, I gained a fuller understanding of a cognitive effect that I’ve been exploring recently (see this paper), the ‘goal free effect’.

Discovered by John Sweller, it essentially posits that explicitly trying to solve a problem can result in a lot of ‘attention’ or ‘working memory’ (see here for a discussion of which term to use) being expended in the search process, limiting (or eliminating) the working memory available for ‘learning’ from the actual task. The result is that the problem gets solved, but the problem solver fails to make any generalisations from the solution and won’t be able to necessarily do it again in future.

It doesn’t come across as a a particularly complex theory, but what I’ve been trying to work out is how to make it work in a classroom. I read Pershan’s post but was keen to know more about linking the goal free approach to explicit learning intentions that the teacher has for the lesson (we discuss that here if you’d a bit more detail on this chat).

Sometimes it takes trying something out to get your head around it, and I was determined to do so. This week I encountered a question that I wanted my students to be able to solve, and I thought the goal free effect might be relevant. Here’s the question (see part b):

I recognised that there was a danger here. This was a relatively open question and I anticipated that several of my students would find it difficult. I could anticipate that many of them would just stare at the table without making connections and then after some work time and a few prompts I’d show a solution (or they’d find it themselves in the resource) but, because they’d been so solution focussed along the way, they’d just write the provided solution down and try to memorise it (the provided solution just focussed on the trend for 19 years and under) and fail to see all of the associations that they could have pointed out in the table.

What I did instead was try out Sweller’s theory.

I clipped out the table and showed it by itself on the whiteboard with my projector. I then asked ‘Look at this table… What can you tell me by looking at it? Do you notice any patterns?’

I also gave the following hint: ‘Focus on one row ( ← a row goes like this → ) at a time’.

We then shared as a class and it was an incredibly rich discussion. What I hadn’t anticipated was how asking such a question reduced the barrier to participation for students. I had students point out the patters for each of the age groups, but I also had one student say ‘The years go up in 10s’ as well as another similarly volunteer that ‘The years all end in 6’, this was in addition to associations being found between the year of first marriage and age of first marriage for each of the age categories in the table.

I then gave each student a half sheet of A4 paper and got them to put into words their association (I’d identified from the discussion that students were struggling to put their thoughts into formal mathematics terms, so wanted them to make these descriptions less transient by eliciting a written response) and collected up these bits. I read some out and, as a group, we identified what it was that made the strong ones strong. I hadn’t anticipated this at all, but we ended up making a template for answering these such questions, here it is:

For me this was an incredible experience. We’d made it all the way from an open question to a generalisation, and scaffolded literacy along the way too (I work in a very low SES school with a large English as Additional Language student base, literacy needs are a constant in all classes), something I’d failed to anticipate in my planning.

In carrying out this activity I managed to get a much deeper understanding of how the goal free effect can work, and how it can be tied into a generalisation directly in line with my learning intention for this segment of the lesson (FYI, the explicit learning intention was for them to be able to identify associations from a two-way contingency table then describe the association and back up their claim with data from the table). In future cases, especially when there’s a lot going on in a diagram (see ‘split attention effect’ on bottom left of page 6 in this paper) I’ll definitely have the goal free effect in the back of my mind as one option in my teacher toolbox.

Anchoring for Meaning

In the previous article to this one I wrote about how, in order to remember something new, it’s necessary to link new knowledge to existing knowledge. We called this existing knowledge ‘memory anchors’. There are two main ways that we can link new knowledge to old knowledge. The first is anchoring for meaning and the second is through using mnemonics. This article addresses the former. Anchoring for meaning is a much stronger way of building memory connections than mnemonics is. Anchoring for meaning means we logically connecting ideas in ways that reflect how those concepts are actually linked in the real world*. For example, if you’re trying to learn about derivatives by exploring how velocity is related to displacement, that’s great, because in real life velocity is the derivative of displacement. But if you’re trying to understand the derivative through a mnemonic that you’ve made up about tweedle dum and tweedle dee, it might not stick as well. *The most effective way that I’ve come across of explicitly anchoring for meaning is through the use of concept maps. Above is an example of how the website Hyperphysics helps its visitors to anchor for meaning when learning about Quantum Physics. Hyperphysics is an amazing site and whenever I want to know anything about Physics (eg: Newton’s Laws) I usually just type into google “Newton’s Laws Hyperphysics” and there’s a high chance of getting a great summary. But it’s not just sticking power that makes it important to anchor for meaning when possible. It’s recollection power. In order to store your memories in a way that they’ll get cued at a relevant time, it’s really helpful to store them in a logical way, and the most logical way is by meaning and logical connections. To expand upon our derivative example above, if you learn about the derivative as linking displacement and velocity, then when you come across a question asking you to explore how velocity and acceleration are linked, you’re more likely to think that the derivative may have something to do with it (and you’d be right!), but if you’ve managed to get the derivative concept stuck into your brain via the tweedle dum and tweedle dee mnemonic, the ‘relate velocity to acceleration’ question will more likely leave you in wonderland… This fact, that anchoring for meaning means that your memories will be cued at the optimum times is part of a bigger principle. This principle is encapsulated by Daniel Willingham with the phrase “How You Think Determines How You Remember”

How You Think Determines How You Remember

Let’s play a game! Try to remember the objects in capitals (not bold) from the following 3 sentences

The violin player lugged the heavy PIANO up the stairs.

The car salesman took a bite of a juicy APPLE.

The WALKING STICK was leant upon by the retired sword fighter.

The boy cracked the EGG when he fell off the fitness ball.

The vampire was passed right through by the GHOST.

Below I’ve provided 2 sets of clues to remind you of the key words in the list above. Scroll down so you can no longer see the above list and start by reading the first set of clues. Try to use them as a basis for remembering the 5 objects.

How did you go? Maybe you got all 5? If you did, well done! If not, maybe this second list will help a little bit more…

Clue set 2: Something that’s heavy, Something that’s juicy, Something you lean on, Something that cracks, Something that can pass through other things.

If the above example 1 worked well then you will have found the second list much more helpful. Perhaps the first set of clues even made you remember a wrong word from the list! Whilst the first set of clues were all valid clues, the clues didn’t mirror the way that you thought about the objects in the first place (ie: the way the sentences described them such as a juicy apple rather than a red apple). This is because as anything makes its way from short term to long term memory, the way that it’s thought about whilst in that transition phase influences how it’s remembered/encoded and thus, what brings the memory back.

There is one key lesson in this for teachers. When we’re designing a lesson plan, and trying to spice it up for students it is VITAL that we ask ourselves ‘what is this activity actually going to make the students think about‘. If we try to teach students about the history of aviation by getting them to make model airplanes, chances are what they’ll remember from the lesson is who they managed to hit with their plane rather than who the Wright brothers were. As teachers, our goal is to get students to think about meaning. It’s important that, when we can, we introduce content in a way that emphasises its meaning.

What to do when Anchoring for Meaning isn’t Possible

There are times when it simply isn’t practical to anchor for meaning. This could be if:

You’re starting a learning project into an area where you don’t know anything at all yet – eg: If you start to learn a language that seems extremely detached from you own, like Chinese.

You haven’t built up the required background knowledge to make links in a logical way yet, and/or you simply don’t have time to do it – maybe you’ve been slacking off all semester and the test is coming up!**

If there simply isn’t a logical reason why the piece of information is the way that it is – eg: you meet someone and you want to remember their name. (There’s usually no logical reason why a person has a certain name, and even if there was one for their parents, there’s no guarantee that it will seem logical to you!)

In cases like these we need to revert to a secondary way of anchoring. Mnemonics! Mnemonics refers to a whole suite of memory techniques that can be used when, for whatever reason, you can’t manage to Anchor for Meaning. Learn about mnemonics in the next article in the memory series, here.

**BEWARE. Often we can use mnemonics to cut logical-learning corners, but in the long run this only serves to handicap us. The more genuine facts you know about a topic, the easier it is for you to learn more about that topic. If you get into the habit of linking things that you learn to your prior knowledge in abstract ways, you’re rate of learning is going to be compromised further on down the track. When you’re dealing with subjects where there are logical connections to be made (Maths, Physics, etc) it really is in your best interests to take the time to lay down solid foundations and to REMEMBER those foundations.

Notes:

Inspired by the example in Why Students don’t Like School by Daniel Willingham. Kindle location 1092.

From Why Students don’t Like School by Daniel Willingham. Kindle location 969.

This is the ‘guiding principal’ in chapter 2 of Daniel Willingham’s Why Students Don’t Like School. I’ll start by pointing out that this title for Willingham’s book is a bit misleading and the subtitle ‘A cognitive scientist answers questions about how the mind works and what it means for the classroom’ gives readers a much better idea of the book’s content.

Willingham’s book is an excellent overview of 7 crucial cognitive principals that are of great value to anyone who is interested in teaching and learning. In fact, the book in large part inspired this set of posts (of which this is the first) for me and I’ll be going over each principle in detail in the coming weeks.

Of all of the lessons in the book, this one was for me the most profound.Why? For many years I have been of a certain mind that “we are wasting our time teaching kids facts at school, what we need to be teaching them is how to learn and how to think critically!” Whilst I still firmly believe that learning how to learn and critical thinking are… critical, this chapter helped me to realise that:

“Data from the last thirty years lead to a conclusion that is not scientifically challengeable: thinking well requires knowing facts, and that’s true not simply because you need something to think about.The very processes that teachers care about most—critical thinking processes such as reasoning and problem solving—are intimately intertwined with factual knowledge that is stored in long-term memory (not just found in the environment).”-kindle location 552

…It’s all to do with working memory. Here’s (my elaborated version of) “Just about the simplest model of the mind possible” that Daniel introduces in Chapter 1. Let’s talk through it

When we begin to solve a problem, 3 windows of our mind are engaged, The environment, our working memory, and our long term memory. The environment is where the question is posed, it’s also where we have access to other information like youtube clips, formula sheets, the working of the kid sitting next to us, and so on. Long term memory is where we store all of the stuff that we’ve already learned. Working memory is where the processing happens. So when we solve a problem we can draw both from our long term memory and from the environment to come up with the solution. If that’s all there is to it then theoretically we should be able to solve any problem as we have access to a seemingly limitless amount of information, but there’s a catch, your working memory only has about 7 slots. 7 precious slots with which you can work*. The reason why long term memory (knowing stuff) is so important is that by remembering stuff you can compress many individual pieces of information and concepts (represented above as pink blocks) in such a way that they only take up one slot in working memory (ie: 1 blue block=many pink blocks). This process is called Chunking and it frees up working memory space for additional info and processing facilitating higher order and more complex thinking. This has important implications for teaching/learning techniques such as the use of formula sheets and scaffolding.

* (7 plus or minus 2 slots covers the majority of the population)

For an example of this please see the bottom of this page.

This information has completely changed my view of what it means to ‘learn’ something…

“I don’t have to memorise anything because I can just put it onto my formula sheet.”

This was my mindset throughout the majority of my undergraduate degree in Physics. See the picture below for an example of one of these such sheets (which we were permitted to take into exams).

After reading this chapter of Willingham’s book I now better understand why I found some parts of my degree as challenging as I did. My ‘I’ll just put it onto my cheat sheet’ mentality was actually preventing me from taking my Physics to the next level. The 7 slot limit of my working memory was being overwhelmed. I hadn’t memorised important facts and info sufficiently for me to ‘chunk’ them, which was limiting my ability to combine concepts in creative ways to solve problems. This conclusion has opened my eyes to the importance of storing things in long term memory and from now on I’ll be making a more concerted effort to use programs such as Anki to do just that! (also the reason why I’m changing my Wot-I-Got blog post format and will be introducing more mnemonics to help readers/my self to better remember blog post content in future).

Conclusion

So, are facts more important than critical thinking? Well… it’s more that facts are a precursor to critical thinking. Knowing facts frees up the processing power of your brain to analyse new information as it comes in.

But this isn’t the only reason why learning facts is super important. Another reason is because knowledge is like money, the more you have the easier it is to get. This is the topic of the next post in this series (coming soon).

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An example of how we’re limited by our 7 slots.

Let’s consider the importance of knowing stuff with an example.

Q: If the nightly revenue of a restaurant is represented by R=-20c2 + 200c + 1920 (where c is no. of customers per night) use calculus to find the maximum nightly revenue.

Without being too exhaustive let’s list some of the things that someone would need to know to answer this question. (think of each number as a pink block)

How to read

What a restaurant is (etc, etc, etc with the really obvious stuff)

what revenue is

that c2 means that it’s a quadratic

that a quadratic equation has a gradient

That the turning point of a quadratic is when the gradient = 0

How to take a derivative

How to set a derivative, R’, equal to 0

Basic algebra to isolate C once you’ve set R’ equal to 0

That that’s the number of customers that would generate maximum revenue

that the R equation relates the number of customers to the revenue associated with that many customers

That you can sub C into the R equation to calculate to find the maximum nightly revenue possible

Now, to me that looks like more that 7 pink blocks. For pretty much all students we can conclude that they have combined pink blocks 1 and 2 (ie, all the obvious stuff) into a blue block, but after that it’s still clear that other stuff must be ‘known’ in order for them to successfully complete the problem, especially if one of their 7 working memory slot is being taken up with a “I can’t do this, I’m confused” mantra.

From the above it’s hopefully clear that for a student to successfully solve this problem they must have stored at minimum 6 of the above bits of info in their long term memory.

This is an experimental post format. I’m using a story as a memory device to generate a solid ‘memory anchor’ on which to attach the following information. Hopefully the content of this article will stick in your head better than it would if it was just in text format!

I came across Learning in the Fast Lane when I attended an online webinar with the author, Suzy Pepper Rollins (read about that webinar here). I got so much out of the hour that I thought I’d make the time investment to read her whole book.

No regrets.

Here’s what I got. ..

The LITFL methodology consists of 6 steps that the books walks you through. Here’s an image and associated short story that I’ve put together to help me to remember the methodology.

So, this is the LITFL methodology.

Generate Curiosity: “curiosity killed the cat”. A cat walks into a room

Map Learning Goals: “the cat sat on the mat” The cat sits down on a mat, it’s one of those map-mats that kids sometimes play on

Scaffold: The kids on the mat are building stuff

Vocabulary: As you look closer, they’re building a taxi rank (cabs are in vogue… vogue-cab-ulary ; )

Apply: One of the kids applies pressure to the cat’s tail!

Feedback: A parent comes in and provides some feedback to that child!

Now look back up at the picture and link all of the concepts to the images, play the story over in your minds eye, and see if you can recall all of the 6 steps with ease.

Here’s those same points in Suzy’s words.

Generate thinking, purpose, relevance and curiosity

Clearly articulate learning goals and expectations

Scaffold and practice pre-requisite skills

Introduce and practice key vocabulary

Apply the new concept to a task

Regularly assess and provide feedback (ie: formative assessment)

Chapter Layout

In Chapter 1 Suzy outlines this methodology and each of the chapters thereafter delves into detail about each of these elements, and more.

This is one of those books where it’s obvious that the author actually thought about what it would be like to use their book as a resource. Let’s take chapter 5 (on Vocab) as an example. Each chapter begins with a justification of why that chapter exists. Suzy tells us the following at the beginning of Chapter 5 (numbers refer to kindle locations, information paraphrased)

1157: 3-year-olds from welfare families typically have 70%of the vocab of children living in working-class homes (Hart and Risley, 1995)

1184: students need multiple exposures—typically, six—to new words to be able to grasp, retain, and use them (Jenkins et al, 1984)

1194: there is a strong correlation between vocabulary knowledge and reading comprehension. (Vacca & Vacca, 2002)

1204: students have just a 7 percent chance of understanding new words from dense text (Swanborn & de Glopper, 1999)

1220: all students who received direct vocab instruction outperformed those who didn’t. (Nagy and Townsend, 2012)

Great, now we know that vocab matters! Suzy then goes on to the section ‘Strategies to Develop Strong Vocabularies’ and lists 9 different methods of introducing new vocab, she also lets us know that learning with pictures is 37% more effective than just learning off definitions (that’s why I included pics at the start of this blog post!). My favourite one of these 9 methods is the TIP (A poster with Term, Information, Picture on it), which I wrote a bit more about here.

The chapter concludes with a “Checklist for vocabulary development” to ensure that you’re on track and for quick reference.

Every chapter is like this, it covers the Why, How and the What in a way that’s both practical and engaging. I got a lot out of this book and will continue to use it as a resource. I loved getting the whole picture from a front-to-back read but I think it would also be great as a quick reference guide for the educator who’s looking for ‘apply in class tomorrow’ kind of ideas.

See below for my summary notes. There’s a lot of them, it was a super info dense book and excellently referenced. Good stuff!

note: numbers refer to Kindle locations, click the image top right to make the display bigger in another page.

This post is part of an ongoing series entitled “Wot-I-Got”. This series acts as a way for me to share Wot-I-Got out of a book or presentation and whet your appetite for enquiry. It also forces me to finish books that I start, then to review and summarise my conference notes!

This morning I woke before my alarm at 4:43am (Australian Eastern Standards Time) eager to jump into the ASCD webinar on Learning in the Fast Lane, with Suzy Pepper Rollins. Here’s some things that Suzy suggested could be done in classrooms and some of the ideas that her techniques sparked in my mind.

Standards Walls and TIPS: Suzy suggested using Standards Walls. A standards wall is a poster or space on the wall to outline all of the learning goals for a class. But it isn’t just an A4 printout. It’s a big colourful poster that’s constantly evolving and edited by students. It’s acts as a reference for you to say “this is what we learnt last week, and this is what we’ll focus on today” and it provides a context for each lesson, building connections between the numerous concepts in a course. They also provide a framework for assessment and feedback by ensuring that both are in line with the learning goals.

TIPS: Based on the fact that it takes the average student 6 times to learn a word, Suzy suggests a chart with three columns: Term, Information, Picture to help students learn new words. This is better than just a vocab chart because “there’s a 35% increase in retention of words if there’s a picture”. Again, this can be an evolving chart that’s stuck on the wall and acts as a reference for students as you move through content.

An idea sparked: I thought that instead of just adding new terms to the TIP as you introduce them in class you could award prizes or rewards to students who interject your teaching with “TIP” when you use a new term that they haven’t heard before. A teacher could deliberately place certain new terms throughout the lesson and introduce the concept with something like “today you will hear 5 new terms, prizes for anyone who shouts ‘TIP’ first when I say each term for the first time”.

Scaffolding for Rigor: Scaffolding is, in Suzy’s words “plugging holes in the boat whilst moving forward”. The basic idea is that learning today depends on learning in the past, and one of the biggest challenges that students and teachers face when covering new content is the fact that they don’t have the prior knowledge required. “Scaffolding” refers to asking yourself prior to the class “My students could master this concept if only they knew…” then establishing ways to ‘scaffold’ learning by trying to plug these knowledge holes in the lesson. Scaffolding devices that were suggested are bookmarks (students make bookmarks with times tables or the like), posters on the wall, sticky notes and one really original example was a number line posted the ceiling! I must admit, I would have loved hear about more scaffolding devices for Math particularly and, unfortunately, the webinar didn’t have time to get to my question of “How do we scaffold for holes that are really big?” eg: the student still can’t do algebra!

Success Starters: Suzy mentioned that in the book How the Brain Learns Mathematics by David Souza, David suggests that students remember what’s covered mostly in the first few minutes and in the last few minutes of a class. The idea of a “Success Starter” is it’s like a warmup but it’s content focused to take advantage of those vital learning minutes at the start of a class. Students can never take in all of the information that they encounter throughout the day, so they are constantly selectively deleting information and (consciously or unconsciously) asking themselves questions like “what’s this got to do with me?” and “will I have a good chance of being successful at learning this?”. Some examples of Success Starters are doing a survey that’s related to the class content or getting students to do an “Alphabetic Brainstorm, essentially trying to think of something that starts with A, B, C, D, etc (you can restrict the range to keep the task shorter) that’s related to one of the concepts that you’ll be covering during the day. This also links to Suzy’s suggestion that one of the biggest determinants of success in class is prior knowledge. So alphabet brainstorms really tap into that prior knowledge and share it around with the wider class.

An idea sparked: I thought that a good success starter could be to have different tasks or questions on different tables, and get students to walk around the room and look at the questions and decide to sit at the table with the question that they’d most like to address, or the piece of information that they would most like to learn. Alternatively, you could run a pop quiz 5 minutes into the lesson, but don’t call it a pop quiz, call it a “peep quiz” , and the students actually have the answers to the quiz sitting on their tables when they walk into the room and they have 5 minutes to peep the answers before they do the quiz. This could be used well in a summary class where the remainder of the class could be used to focus on points that the students struggled with in the peep quiz.

See what they’re doing minute-by-minute, Formative Assessment: Many readers will be familiar with formative assesment so I’ll just point out the techniques that were suggested in the webinar:

Bow Tie: Get work on a task together on a big ‘bow tie’
where the centre acts as a space for consensus answers (see pic)

Sorts: Sorts are getting students to sort information (often presented on small cards) to promote discussion about categories and aid comprehension

Cubes: Teachers can make ‘cubes’ that have questions (or components of questions) on them and students can roll the cubes to introduce see which question to do next (or to make up a question. Eg: multiply the number on the first cube by the no on the second)

An Idea sparked: I’ve been thinking about employing Flubaroo in the classroom for a while but I had 2 ideas of how to make this a bit smoother.

Firstly: Get students to only enter their answers into the google docs solutions page at the end of the test, give them 3 mins or so to do this. This has multiple benefits

students won’t get distracted by their computer during the test

their writing will have to be tidy so that they can see what they did

this forces them to look back over their working and answers

It would help to avoid them googling answers (due to the limited time)

The teacher could sit at the back of the class and watch screens for this short period of time

Secondly: Double tests in one class! Test students once, and aportion some level of value to the first test, then you use the feedback from that first test instantly motivate them to learn to study hard and fast for a second test (may be better for tests for which marks aren’t recorded as don’t want to put too much pressure on students). Furthremore, the info from test 1 could allow a teacher to match up students that got the answer right with students who could do with a little help (for the qs where there is a balance of correct and incorrect answers). For the Qs where lots of students need help, a teacher could go over the process on the board for the whole class’ benefit.

Self-Efficacy Development: It was suggested that a teacher should consider the following when trying to build self efficacy among students

level of difficulty of the task

value of task (perceived and real)

Incorporate choices and social interactions into learning

compelling openers that build success (see “Success Starters” above)

safe for mistakes (try to foster a culture of sharing in the classroom)

short term goals (keep learning goals relevant and today)

ongoing, quick feedback (see “See what they’re doing” above)

Building self-efficacy among students remains one of the biggest and most important challenges for teachers. Unfortunately, with the 4 or so minutes that we had a the end of the webinar to cover this point we weren’t able to go into that much depth.

Summary: I found the webinar extremely insightful and Suzy’s enthusiasm and obvious experiences of success were really inspiring. I found the learning in the fast lane approach to be a useful collection of practical suggestions for the classroom and particularly like how teachers can pick and choose which elements of the approach to implement and which to leave out. It isn’t an “all or nothing” model.

A great summary of the the collection of articles that form the pedagogical basis for the Learning in the Fast Lane model can be found here.